Iphone without battery if off, always turns on when you plug it in. However if it is on when you plug it in, you can always shut it off after you plug it in.
With the new battery pack attached, and while on "battery power" if you turn your phone off, it shuts off, however after it is off for a few seconds, it powers back on.
Is there anyway to shut the phone off without having to remove it from the charger case?

Is the iPhone 7 Smart Battery Case the same as Phone 7 and iPhone 7 Plus which are splash, water, and dust resistant and were tested under controlled laboratory conditions with a rating of IP67 under IEC standard 60529?

Yes you need to charge it - it has a lightning port at the bottom of the case which you plug your charging cable into, this simultaneously charges the case and the phone (if inserted). If it's the same as the iPhone 6 battery case then you can also charge the case without a phone inserted (you can see a little led within the rear cover (normally hidden by the phone) which indicates if the case is fully charged or not.